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Mea culpa, I guess. (Though I didn’t write the title, and certainly won’t take any responsibility for the comments!)

From my perspective, the story is this: if you want to get difficult mathematical ideas in the broader press – and I do – then you have, to some extent, to play by their rules. I think it’s fair to say that mathematicians generally are highly cautious about the claims they make, and cover everything in caveats. That’s not a criticism, because it’s my natural tendency too, but if you take that approach in the wider media, you will get nowhere. At the same time, I am well aware of the dangers of a combination of dumbing down and hyping up. So, as in all things, one strives for balance.

To put it another way, whenever I write about maths in the press, there are two types of response that are guaranteed: firstly people complaining that my article is far too dry, overly technical, and generally incomprehensible. The other is from mathematicians complaining about oversensationalisation. I might facetiously comment that if the number of each are about equal, then I probably judged the balance about right.

So – and I would genuinely be interested in the answer to this question – is there any part of the article where you think I crossed a red line? I am, after all, always looking to improve as a communicator of mathematics.

(Incidentally I make no apology for finding Friedman’s concrete arithmetical statements, with provability strength at the the level of large cardinals, exciting and worthy of reporting. But if you disagree I would of course be interested to hear why.)

your article is excellent — as an article for general public. My blog is aimed at mathematicians, and therefore I write from different positions. I have a challenge now: I have to try to write an explanation for mathematicians outside of logic and set theory of what Friedman actually done.

I now systematically write semipopular texts about infinity, and know how difficult was your task. I have nothing but admiration of your work. My main issue: how to get messsage through to people who wrote commentaries on your paper?

I am sorry if I seemed unnecessarily defensive, perhaps I understood criticism where none was intended. (Of course, I would not be offended by criticism though, as the balance is difficult to strike, and I’m sure I do sometimes get it wrong.)

As to your challenge – I will be very interested to read the result! I have also written about Friedman’s work at a higher level of technicality – approximately that of a general mathematical audience – on my blog (see also the slides there of a talk I recently gave).

It would be good to be able to get the message through to the commenters on the piece, but I fear it is a dream… I have already received one letter to the paper’s editor, containing a ‘refutation’ of Cantor’s theorem, and I am sure there will be others….